Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

Abstract

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

Keywords

• Large Deflection
• Beam
• Combining Method
• Finite Element Method
• Functionally Grade Material

Fonksiyonel Dereceli Kirişin Birleşim Metodu Kullanılarak Büyük Sehim Analizi

Öz

Bu çalışmada dairesel kesitli bir kirişin büyük sehim davranışı Birleşim Metodu (BM) kullanılarak incelenmiştir. BM, Matlab-Simulink programındaki blok diyagramları ve Diferansiyel Quadrature Metodundaki (DQM) ağırlık katsayılarını kullanan sayısal bir çözüm yöntemidir. Dikkate alınan kiriş malzemesi Fonksiyonel Derecelendirilmiş Malzemedir (FDM). Kirişin sınır koşulları ankastre-serbest (A-S) olarak alınmış ve kirişin serbest ucundan tekil bir yükün uygulandığı varsayılmıştır. Kirişin büyük sehim denklemleri hesaplanırken ve sayısal analiz yapılırken geometrik doğrusal olmayan analiz yapılır. Kirişe uygulanan kuvvetin arttırılması, kiriş kesitinin boyuna yönde değiştirilmesi ve FDM'nin malzeme indisinin değiştirilmesinin kirişin aşırı sehim davranışı üzerindeki etkileri incelenmiştir. Karşılaştırma amacıyla BM'den elde edilen sonuçlar hem SolidWorks-Simulation hem de Ansys-Workbench programlarından elde edilen sonuçlarla karşılaştırılmıştır.

Anahtar Kelimeler

• Büyük Sehim
• Kiriş
• Birleşim Metodu
• Sonlu Elemanlar Metodu
• Fonksiyonel Derecelendirilmiş Malzeme

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